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I have a doubt regarding behaviour of ferromagnetic material. I know that magnetic fields are said to increase in intensity inside bulk of ferromagnetic material, or converge into them.

Does this mean or imply that magnetic field intensity B decreases in the region surrounding the ferromagnetic material than what it was when ferromagnetic material was absent?

Here in the image does magnetic field instensity decrease in region below and above the iron piece?

enter image description here

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Yes. Imagine a horseshoe-shaped magnet with poles at the ends of the bent shoe. Its field lines balloon out from one pole and all are collected together again at the other. Now place a soft iron bar across the gap between the two poles. theTfield is now propagated inside the iron bar and if the horseshoe and bar are cleverly shaped and trimmed, no net field at all will emerge from the assembly.

The art of arranging magnets and pole pieces inside a motor or generator in such a manner as to minimize the propagation of a magnetic field outside it (which is useless from the standpoint of operating the motor or generator) is called flux leakage prevention.

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Yes, it does decrease outside of the iron piece. Imagine the new magnetic field introduced by the iron piece (would look like a bar magnet). When superimposing with the original magnetic field, you'll find cancellation outside the iron piece.

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